# Category Archives: science

## Natural Selection = Fitness × Acceleration

Natural Selection is the force that changes species.

Fitness is the resistance to change in the rate of change of the species.

Acceleration is change in the rate of change of the species.

Natural Selection = Fitness × Acceleration

Posted in biology, evolution, fitness, philosophy, science. Tagged with , , , , .

## Rewrite of Evolution

New theory of evolution!  Hooray!

Patched a bunch of things together to make a nice story.  Fixed the little issue about fitness being circular.  Expanded natural selection to apply more generally.  Causal structure.  Epistemological foundations.  ooOoOO0Ooooooo.

And it’s good fun.  I swear.  Epistemology, history of physics, evolution… makes me happy.  You should really read it.

## Revision and Hypothesis Introduction

Say we have some theory that we represent with a formula of logic.  In part it looks like this:

[1] …(∃z) … Pz …

This says that at some point in the theory there is some object z that has property P.

After much hard work, we discover that the object z with property P can be described as the combination of two more fundamental objects w and v with properties R and S:

[2] …(∃z) … Pz … ⇒ …(∃w)(∃v) … (Rw & Sv)…

Now lets say that in our theory, any object that had property P depended upon some other objects, x and y:

[3] …(∀x)(∀y)…(∃z) … Pz …

In our revised theory we know that objects w and v must somehow depend upon x and y, but there are many more possible dependence patterns that two different objects can have as compared to z alone.  Both w and v could depend upon x and y:

[4] …(∀x)(∀y)…(∃w)(∃v) … (Rw & Sv)…

However, let’s say that w depends on x but not y, and v depends on y but not x.  Depending on the rest of the formula, it may be possible to rejigger the order of the quantifiers to reflect this, but maybe not.  If we allow ourselves to declare dependencies and independencies, arbitrary patterns of dependence can be handled.  The forward slash means to ignore the dependency of the listed quantified variable:

[5] …(∀x)(∀y)…(∃w/∀y) (∃v/∀x) … (Rw & Sv)…

Besides the convenience and being able to represent arbitrary dependence structures, I think there is another benefit for this use of the slash notation:  theoretical continuity.  In formula [2] above, there is a double right arrow which I used to represent the change from z to w and v, and P to R and S.  However, I created this use of the double right arrow for this specific purpose;  there is no way within normal logic to represent such a change.  That is, there is no method to get from formula [3] to formula [4] or [5], even though there is supposed to be some sort of continuity between these formulas.

Insofar as the slash notation from Independence Friendly Logic allows us to drop in new quantified variables without restructuring the rest of the formula, we can use this process as a logical move like modus ponens (though, perhaps, not as truth preserving).  Tentatively I’ll call it ‘Hypothesis Introduction’:

[6]

1. …(∀x)(∀y)…(∃z) … Pz …
2. …(∀x)(∀y)…(∃w/∀y) (∃v/∀x) … (Rw & Sv)…      (HI [1])

The move from line one to line two changes the formula while providing a similar sort of continuity as used in deduction.

One potential application of this would be to Ramsey Sentences.  With the addition of Hypothesis Introduction, we can generalize the Ramsey Sentence into, if you will, a Ramsey Lineage, which would chart the changes of one Ramsey Sentence to another, one theory to another.

A second application, and what got me thinking about this in the first place, was to game theory.  When playing a game against an opponent, it is mostly best to assume that they are rational.  What happens when the opponent does something apparently irrational?  Either you can play as if they are irrational or you can ignore it and continue to play as if they hadn’t made such a move.  By using Hypothesis Introduction to introduce a revision into the game structure, however, you can create a scenario that might reflect an alternate game that your opponent might be playing.  In this way you can maintain your opponent’s rationality and explain the apparently irrational move as a rational move in a different game that is similar to the one you are playing.  This alternate game could be treated as a branch off the original.  The question would then be to discover who is playing the ‘real’ game – a question of information and research, not rationality.

Posted in game theory, independence friendly logic, logic, philosophy, science. Tagged with , .

## … Yeeeeaaaaaaahhhhhhh

via BackRe(Action)

Posted in fun, General Relativity, measurement, physics, Relativity, science, Special Relativity. Tagged with .

## Hypotheses Natura Non Fingo

Newton famously wrote [1] [2]:

I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses…  It is enough that gravity does really exist and acts according to the laws I have explained, and that it abundantly serves to account for all the motions of celestial bodies.

as a response to those who challenged him to provide causes of gravity.  He said, “Hypotheses non fingo,” or, “I feign no hypothesis,” or if you will, “I haven’t even a guess.”

Earlier in a letter he wrote:

That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.

These passages show that Newton recognized a fundamental causal problem within his theory: that although his mathematics described gravitational physics, it did not provide a causal explanation.  It was not until General Relativity 200 years later was this problem solved.

Recently another major fundamental theory of science has been accused of lacking the proper causal structure:  Fodor & Piatelli-Palmarini’s attack on evolution, What Darwin Got Wrong.  Consider what Fodor says in his recent reply to Block and Kitcher,

A mere chronicle of instances of adaptation would not therefore amount to a theory of adaptation. It would just be “natural history.” We haven’t the slightest doubt that Darwin thought that he had discovered a theory of adaptation. It was, to be sure, a pretty thin theory, as it would have to be in order to apply to evolving creatures as such, whatever their phenotypes and whatever their ecologies.

He is saying that evolution is a mere chronicle of natural history — not a cause of it — just as Newton’s gravitation described gravity without revealing its causal structure.  Later he says,

[Biologists should] give up on the project of finding a mechanism for evolution and study the fixation of adaptive traits case by case. Since all the evidence suggests that they are extremely heterogeneous, this should keep evolutionary biologists busy well into the indefinite future.

This means that biologists should give up on repairing evolution and just try to explain individual phenomena moving forward, just as physics moved forward even as Newton knew his theory was on metaphysical shaky ground.

Hence it is Fodor now saying, “Hypotheses non fingo,”  because he believes he can describe natural history accurately, but also has no guess as to what caused things to work out the way they did.

* * * * *

In light of this analysis, consider this statement from Block and Kitcher’s counter argument:

After our critique, Fodor and Piattelli-Palmarini have apparently decided that the crucial point is the lack of a “theory” of natural selection. But, as we have noted here, nobody needs a “theory” of the type they demand.

And this from Sober’s recent review [pdf]:

What is the net gravitational force now acting on the earth?  That depends on the mass of the sun, the moon, the stars, and of everything else.  It does not follow that there are no laws of gravity, only that the laws need to have numerous placeholders.  FP may object to my analogy because it is always the mass of these various objects and their distance from the earth that are relevant to the gravitational force that the earth experiences.  My reply is that this makes no difference…

Neither has understood the argument as presented above.  If Block and Kitcher had understood, then they would have recognized that yes, for the vast majority of people, the “‘theory’ of the type they demand” is unnecessary, but it is, nevertheless, of critical importance to the likes of Newton and Einstein.  If Sober had understood, then he wouldn’t have used the worst possible example to make his point:  by saying it is “always the mass of these various objects and their distance from the earth that are relevant,” and not mentioning motion, we know he was only thinking about Newtonian Mechanics.

* * * * *

Should we, with Fodor, believe that we are stuck in a philosophical absurdity?

No.  What I said in my original criticism of Fodor, found in What Fodor Got Wrong (18 March 09),  still applies.  Though the above description of the problem is likely clearer than my analysis based on his claims that Natural Selection is statistical and that the struggle for survival is only a metaphor, the problem of causal structure is the same.  My solution focuses on using individual struggles as local interactions of Natural Selection — like a gravitational field in General Relativity — and hence provides the causal structure that Fodor wanted.

[EDIT 6 April 2010:  I’m thinking I gave Fodor too much credit in this post.  I now think his arguments amount to saying that for each instance of evolution we have, we are merely relaying natural history, not a causal explanation.  The argument I attributed to Fodor above says that evolution by natural selection is natural history.  Fodor must be more agnostic about evolution’s ontology because of how he says it is possible to look for some alternative to natural selection in his reply to Block and Kitcher.  My solution is still viable though:  since I provide causal structure, this also provides how to describe evolution in a causal way.]

Posted in biology, evolution, General Relativity, philosophy, physics, Relativity, science. Tagged with , , , , , , , .

## Against Physics as Ontologically Basic

1.  Biology is epistemically independent of physics:

Let’s assume that biology is not epistemically independent of physics, i.e. to know any biology we must first know something about physics.  However, consider evolution as determined by natural selection and the struggle for survival.  We can know about the struggle for survival and natural selection without appealing to physics — just as Darwin did when he created the theory — and hence we can fundamentally understand at least some, if not most, of biology independent of physics.

2.  Physics supervenes on biology:

Whatever ability we have to comprehend is an evolved skill.  Therefore any physical understanding of the world, as an instance of general comprehension,  supervenes on the biology of this skill.

3.  Biology is just as fundamental as physics:

If the principles involved in biology and physics are epistemically independent and each can be said to supervene on  the other, then neither has theoretical primordiality.

Therefore physics is not ontologically basic.

.

.

[This argument was inspired by a discussion over at It’s Only a Theory start by Mohan Matthen.

And I want it to be known that I HATE SUPERVENIENCE.  Basically if you use supervenience regularly then you are a BAD PERSON.  The only good argument that uses supervenience is one that reduces the overall usage of the word:  it is my hope that the above argument will prevent people from saying that biology supervenes on physics.  For every argument in which I thought that using supervenience might prove useful, I found a much, much superior argument that did not make use of the term.  I know you always live to regret statements like this, but right now I don’t care.]

Posted in argumentation, biology, epistemology, evolution, ontology, philosophy, physics, science. Tagged with , , , .

## Fodor May Yet Be Clever

I was trying to figure out what Fodor could have been thinking.  Here’s what I came up with:

1. If we are trying to figure out what Evolution has done, then we presuppose that Evolution is capable of doing something.
2. If Evolution is capable of doing something, then there must be some mechanism of Evolution that does the doing.

Now imagine yourself in the position of the mechanism of Evolution that does the doing, i.e. the mechanism that selects the traits that yield a higher fitness.

The question becomes: is it possible for you to select for a trait?

To understand why, consider what happens when we try to give an evolutionary explanation of something:  we are beset by a near infinite selection of different possibilities.  Only through careful study can we narrow down which traits are actually the ones that increase an organism’s fitness and, if we are in a historical context, only give a most likely candidate for such a trait.

Now imagine yourself back in the position of the mechanism.  The mechanism is stuck with the exact same sort of problem that we have when trying to figure out what it has done:  it has no more an ability to select a single trait than we have to figure out which trait it has selected with our first guess.  Whenever it tries to select for a trait, it may mistakenly also select for another trait that is not so good for the organism, or it may not have even recognized the trait it thought it was selecting for.

Therefore, since this mechanism can’t work, evolution is bunk.

OK.  Now let’s take a step back and look at this argument.  Basically there are two parts:  the first part is an argument that there is a mechanism that does the doing and the second part says the mechanism can’t have done anything.  When I saw Fodor speak on this topic, I believe (it was a while ago now) he spent a good deal of time on arguing for the first part and I didn’t really understand what he was up to.  Now it makes sense because if we accept that there is some mechanism that does the doing, then we may be committed to admitting to at least some amount of skepticism about evolution based upon the second part.  Getting even some skepticism about evolution would be a sufficiently large accomplishment, and so I figure this must be Fodor’s ultimate goal.

In light of this argument I offer this wild conjecture for your reading pleasure:

Replace “mechanism” with “agent”.  Now, instead of an argument against evolution, it is an argument against Intelligent Design.  Intelligent Design has the designer/ agent built directly into it, and this makes the argument much more knock-down:  There is no need to argue for the existence of a mechanism because it is right in the title, and since the intelligence of ID is something like our intelligence, it makes sense that it would suffer from the same problems that ours does.

What I think happened is that Fodor was sitting around thinking why intelligent design doesn’t work and realized that if he could make a strong enough argument that evolution also required some sort of agent, in the form of an evolutionary mechanism, then he could return a similar result.  Since having a technical reason for discounting ID wouldn’t make much of splash, Fodor dropped the argument against ID and pursued the argument against evolution.

Personally I kind of like this argument against ID.  If I ever run into some ID people, I may even bring it up.

## Fodor’s Intensional Criticism of Evolution

Fodor’s intensional criticism of evolution is that the process of evolution is unable to make the necessary distinctions in selecting traits.   This is to say that evolution itself cannot  select for specific traits.  If evolution can’t select for traits, then we will definitely not be able to figure out what’s happening based on evolution.  Hence evolution is not a good theory.

Does evolution need a mechanism to select for certain traits?

No, there is no need for a mechanism which decides that it wants a certain trait and then systematically selects for that trait.

Instead evolution is more like a Plinko / Pachinko machine with moving pins and prize locations.   Organisms – the balls – live and die by bouncing off whatever exists in their environment – pins and prizes -.  Whoever happens to land in a good location gets to have their genes replicated.  In this setup there is no need to appeal to some evolutionary mechanism to select traits because  with the environment and organism described, the evolutionary traits that will be selected are probabilistically determined.

Our evolutionary explanations, then, describe the environment – the position of the Plinko pins and prizes – and the biology of the organism – the shape and location of the Plinko ball – to show why that organism ended up in a position to replicate.  If we want to describe how we evolved to have hands, for example,  we show how organisms that more consistently landed in the right locations had the traits that led to us having hands, and not because there was a mechanism to pick out ‘having hand traits’ at the start.

Therefore Fodor’s argument from intensionality is a straw man:  Evolution does not need to be able to make the distinctions that Fodor says it needs to make.  Hence there is no problem within evolution.

[EDIT:  I’ve put up a new analysis (24 March 2010) of Fodor’s argument here: Hypotheses Natura Non Fingo]

For my take on what else Fodor got wrong, see my post What Fodor Got Wrong (which this argument actually presupposes), and the follow up Dismantling Fodor’s Argument.

Posted in biology, evolution, philosophy, science. Tagged with , , , .

## On Block and Kitcher on Fodor

Ned Block and Philip Kitcher have posted a review of Fodor/Piatelli-Palmarini’s “What Darwin Got Wrong” (via Leiter).

It is a well executed, though flawed, counter to Fodor’s arguments.  First they give a nice rundown of the underdetermination issue I posted about here.

Then they discuss the “intensional fallacy”.  They argue that the crux of F & P’s argument can be seen as trying to split up the causal efficacious trait and the selected-for trait.  This means that F & P believe that there is no way to connect the evolutionary reason – the trait that increased an organism’s fitness – with our explanation of the trait that was selected-for.  Block & Kitcher argue that it is trivial to match the two up because

selection-for is a causal notion, and, since causation is extensional, so is selection-for.

Insofar as we believe that our explanation of the selected-for trait is extensional, i.e. truth-preserving when switching between different names of the same thing, we can say that we do pick out the causally efficacious trait.

Unfortunately Block and Kitcher sacrificed our normal concept of explanation to make this counter-argument.  They note that explanations are never normally extensional, but that we are making an exception in this case.  This is ok to do because

we thinking beings can give (intensional) explanations in terms of [one trait] rather than the other properties. In giving the explanation, we (thinking beings) describe the property in our preferred way.

I do not understand what is going on here.  Basically it looks as if “preferred way” is just a fancy way to say “own words”, but describing something in our own words doesn’t make it right.  Nor is it a reason to change what should count as an explanation.

Unless Block and Kitcher are prepared to give further justification as to why we should disregard our normal understanding of explanation, it looks as if their solution to Fodor’s argument is ad hoc.  They are using explanation* — which is a special kind of explanation that can be extensional — but they have not given a reason why explanation* should be preferred over of regular explanation (outside of causing Fodor trouble).  Without this reason, the use of explanation* is ad hoc, and hence the argument fails because it turns on an ad hoc premise: the assumption that explanation* can be substituted for explanation.

However, I did say above that Block and Kitcher’s argument is well executed:  My argument against using an ad hoc term-term* distinction is obscure compared to their argument and so, for the vast majority of people, it will appear that their argument is effective.  Overall this is a good thing: less nonsense needs to surround evolution (though I’ll be a little sad to see it go: I’m #1 in a Google search for “fodor what darwin got wrong“).

[EDIT:  I’ve put up a new analysis (24 March 2010) of Fodor’s argument here: Hypotheses Natura Non Fingo.  It also includes a review of the responses of Block, Kitcher and Sober ]

For my take on what Fodor got wrong, see my post What Fodor Got Wrong, and the follow up Dismantling Fodor’s Argument (also linked above in reference to underdetermination).  I’ll post something soon specifically addressing the intensionality issue:  Fodor’s Intensional Criticism of Evolution.

Posted in argumentation, biology, evolution, fitness, news, philosophy, science. Tagged with , , , , , .

## Aristotle’s Theory of TOPOS (Place)

[This is something I wrote before I had this blog, but I really like it and hope the readers here will find it interesting.]

The task of explaining Aristotle’s theory of place lies in the interpretation of this sentence: “Hence the place of a thing is the innermost motionless boundary of what contains it,” (Physics IV 212a20).  Now the idea of a motionless boundary for perceptible and obviously movable objects seems impossibly counterintuitive.  However, using Aristotle’s comments into the nature of place, we can understand how this theory extends beyond a simple boundary theory and into the modern era.

His discussion is started by making an observation:

The existence of place is held to be obvious from the fact of mutual replacement.  Where water now is, there in turn, when water has gone out as from a vessel, air is present; and at another time another body occupies this same place.  The place is thought to be different from all other bodies which come to be in it and replace one another.  What now contains air formerly contained water, so that clearly the place or space into which and out of which they passed was something different from both. (Physics IV 208b1-8)

Aristotle then makes some tentative moves into defining what could possibly fulfill the role of place.  First he discounts any idea that place could “be body; for if it were” he says, “there would be two bodies in the same place,” (209a6) and shows how this causes untold amounts of theoretical difficulty (ibid.).  Then he discusses how, as that which “primarily contains each body” (209b1), place could be viewed as the form or the matter.  Again he discounts either of these possibilities by noting that neither of them can be separated from a thing, whereas place may be.

The analysis turns at this point asking, “How many ways one thing is said to be in another,” (210a14) in the hopes of landing upon a useful interpretation of the notion of being-in.  Aristotle entertains the idea that a thing may be in itself, or more specifically, in itself “qua itself or qua something else” (210a27).  He gives the example of a jar of wine being in itself in virtue of the whole’s description in terms of its parts: the jar of wine is not reducible to a jar or some wine, but to their specific combination.  Hence that which is a subject may potentially be a container as well, as the jar is the container of the subject ‘jar of wine’.  However, he says this is impossible as no object is actually like this: the wine would have to be an equal part container, and the jar an equal part wine, else the whole of the ‘jar of wine’ will not be completely in itself.  It is in virtue of being different that the jar and the wine may come together, and hence he concludes that, “since the vessel is no part of what is in it (what contains something primarily is different from what is contained), place could not be either the matter or the form of the thing contained,” (210b27).

Aristotle then considers two sorts of boundary theories.  First, place is such that it is “some sort of extension between the extremities,” (211b7).  However, this sort of boundary exists independently of what is bounded and is permanent.  Insofar as anything moves, the place will change, and there will be two problems generated: 1. The boundary between, for example, the wine and air moving in a jar will be exactly coincident with the boundary between the air and wine, and each of these two boundary extensions will be partially coincident but must also be unique, and 2. There will be a place at the boundary of the displaced place, and so an infinite regress of places associated with previous places will be generated.

Finally Aristotle says, “place necessarily is… the boundary of the containing body at which it is in contact with the contained body,” (212a6).  Then, interestingly, he says, “Place… is rather what is motionless,” (212a17) and then, “Hence the place of a thing is the innermost motionless boundary of what contains it,” (212a20).  So how are we to make sense of containers that give us the boundaries but also do not move?

If we take our interpretation directly from the previous discussion of boundary, Aristotle seems to have made an awfully strange claim: place is a like a container that something perfectly fits in, and yet that container cannot itself move although what is contained therein necessarily can.  However, I would like to suggest taking him at his word in regards to place being necessarily a boundary.  It is necessarily a boundary of the containing body which is in contact with the contained body, but it is not sufficient that it be the boundary that most have in mind.  What has been missed by regarding the boundary as necessary and sufficient is the incorporation of Aristotle’s primary intuition into how we know place exists.

For us to notice any motion we need something stationary relative to the thing moving such that we may observe the motion as motion.  A stationary backdrop is necessary to view change.  Consider this example: it is a common experience to be sitting in traffic next to a bus.  When the bus starts to slowly pull forward sometimes it is possible to get the sensation that you have started to move backwards.  This sensation lasts until some other fact informs you that it was not you who were retreating, but the bus advancing.  In the first instance, the place that you inhabited was defined in terms of a stationary bus: any motion that occurred was relative to that fixed point.  When you realized it was the bus, and not you, that was moving, whatever it was that informed you that you were stationary became incorporated into the place.  Perhaps you saw a building and since it was not moving your senses of place and motion were reevaluated to accommodate this new information. Hence two different places were involved in this scenario: one corresponds to your (belief of) moving backwards and the other to the forward motion of the bus.  The first place has the innermost motionless boundary [illegitimately] defined in terms of the bus [since the bus was in motion], and the second has an expanded sense of place to include something motionless relative to both you and the bus. Place, therefore, not only encapsulates that which is moving, but also whatever is observing the motion and an independently stationary object.

When Aristotle says, “First then we must understand that place would not have been inquired into, if there had not been motion with respect to place,” (211a12) he was not making an idle comment on the ‘discovery’ of the phenomenon of place.  Instead, he was beginning his analysis with the most important feature to be explained.  Galilean relativity holds fundamentally that motion can only be defined relative to some “system of coordinates” (Einstein p. 14), i.e. something motionless with respect to the moving object.  Although Aristotle did not have the benefit of Descartes’ mathematical works he still recognized the need for a reference system unique to each motion.

Now that the meaning of the ‘motionless’ criterion has been explained, what does ‘innermost’ mean if the boundary may include objects at a significant distance from the one we are describing?  The Earth is, in some sense, the place of all sublunary objects, but it is surely not the innermost boundary.  Again appealing to the exact phenomenon that Aristotle was dealing with yields the correct explanation: the motion of an object with respect to its place cannot be described by saying that the place of the thing is Earth.  Instead the innermost boundary should be the first boundary for which the description of motion and place of the thing make sense.  In the example of swirling wine in a jar (with the jar held steady but the wine still moving), the place of the wine can be said to be the jar because it describes the closest motionless boundary.  One might say that the place of the wine is equally on the table, or in someone’s hand, but both of these descriptions are related to motion other than that of wine swirling in the jar, and are really just shorthand for ‘the jar of wine is on the table, or in hand’ (consider, “The wine is on the floor,”: no swirling to be had).  The correct place of the moving bus example was the street, which could reasonably include things such as houses and other stationary objects, the most important one being the road.  Aristotle gives the ancient version of this, just before his final definition of place, in terms of the motion of a boat, such that it must be defined in terms of the whole river, which is taken as stationary (212a19).

One may think that I am being too charitable to Aristotle at this point because it may look that I have implied that the ‘innermost’ criterion of the theory will do all the work of translation between coordinate systems, which it does not seem to do.  However, Aristotle allows for the fact that we may treat a vessel such as a boat as a “transportable place” (212a14).  Hence we may allow for the things within a boat to have motion independent of a preferred fixed reference system.  This connection drawn between vessel and place gives the final aspect needed for a true relativity theory.  Historically the example of a boat on a river (212a19) is striking because Galileo uses the same example of a ship in his Dialogue Concerning the Two Chief World Systems (Salgado).

Commentary

Historically Aristotle’s theory of place has been treated as a simple boundary theory coupled with a few very strange statements that were assumed to be preliminary investigations into different methods of solving blatant paradoxes (King 91).  My suspicion for why this happened is twofold.  First, philosophy of place sounds like the most dry and uninteresting subject possible and hence it was not given its due study time over the course of history (after Aristotle that is).  Secondly, the modern formulation of relativity is given according to Einstein’s theory of Special Relativity.  Insofar as this is a theory of relative motion, it is easy to overlook the fact that it applies to objects without motion, things in place.  Aristotle’s formulation is none the weaker because of the way he cast his theory, but it is much more obscure to the modern reader, as Aristotle’s relativity is developed in a somewhat inverse way with respect to modern relativity.

Bibliography

• Barnes, J. ed. The Complete Works of Aristotle v.2, Princeton U. Press, Princeton 1995
• Einstein, Albert Relativity: The Special and General Theory Lawson trans.  Pi press, NY, NY 2005
• King, H. R., “Aristotle’s Theory of TOPOS,” Classical Quarterly #44 1950, pp. 76-96
• Salgado, Rob “Galileo’s Parable of the Ship” http://physics.syr.edu/courses/modules/LIGHTCONE/galileo.html Accessed 2/24/06 (Link Dead) Archive.org backup, Accessed 16 December 2015.
Posted in philosophy, physics, Relativity, science. Tagged with , , , .